Fibrewise localization and completion

May, J. P.

doi:10.1090/S0002-9947-1980-0554323-8

Fibrewise localization and completion
HTML articles powered by AMS MathViewer

by J. P. May PDF

Trans. Amer. Math. Soc. 258 (1980), 127-146 Request permission

Abstract:

The behavior of fibrewise localization and completion on the classifying space level is analyzed. The relationship of these constructions to fibrewise joins and smash products and to orientations of spherical fibrations is also analyzed. This theory is essential to validate Sullivan’s proof of the Adams conjecture.

References

J. F. Adams, On the groups $J(X)$. I, Topology 2 (1963), 181–195. MR 159336, DOI 10.1016/0040-9383(63)90001-6
Guy Allaud, On the classification of fiber spaces, Math. Z. 92 (1966), 110–125. MR 189035, DOI 10.1007/BF01312430
A. K. Bousfield and D. M. Kan, Homotopy limits, completions and localizations, Lecture Notes in Mathematics, Vol. 304, Springer-Verlag, Berlin-New York, 1972. MR 0365573

ring spaces and their applications

Albrecht Dold, Partitions of unity in the theory of fibrations, Ann. of Math. (2) 78 (1963), 223–255. MR 155330, DOI 10.2307/1970341

Halbexact Homotopiefunktoren

Edward Fadell, The equivalence of fiber spaces and bundles, Bull. Amer. Math. Soc. 66 (1960), 50–53. MR 112137, DOI 10.1090/S0002-9904-1960-10389-8
Henry H. Glover and Guido Mislin, Immersion in the metastable range and $2$-localization, Proc. Amer. Math. Soc. 43 (1974), 443–448. MR 341504, DOI 10.1090/S0002-9939-1974-0341504-4
Daniel Henry Gottlieb, The total space of universal fibrations, Pacific J. Math. 46 (1973), 415–417. MR 331384
Peter Hilton, Guido Mislin, and Joe Roitberg, Localization of nilpotent groups and spaces, North-Holland Mathematics Studies, No. 15, North-Holland Publishing Co., Amsterdam-Oxford; American Elsevier Publishing Co., Inc., New York, 1975. MR 0478146
I. M. James, The space of bundle maps, Topology 2 (1963), 45–59. MR 198472, DOI 10.1016/0040-9383(63)90021-1
Peter J. Kahn, Mixing homotopy types of manifolds, Topology 14 (1975), no. 3, 203–216. MR 377937, DOI 10.1016/0040-9383(75)90001-4
J. M. Boardman and R. M. Vogt, Homotopy invariant algebraic structures on topological spaces, Lecture Notes in Mathematics, Vol. 347, Springer-Verlag, Berlin-New York, 1973. MR 0420609
J. Peter May, Classifying spaces and fibrations, Mem. Amer. Math. Soc. 1 (1975), no. 1, 155, xiii+98. MR 370579, DOI 10.1090/memo/0155
J. Peter May, $E_{\infty }$ ring spaces and $E_{\infty }$ ring spectra, Lecture Notes in Mathematics, Vol. 577, Springer-Verlag, Berlin-New York, 1977. With contributions by Frank Quinn, Nigel Ray, and Jørgen Tornehave. MR 0494077

The homotopical foundations of algebraic topology

John Milnor, On spaces having the homotopy type of a $\textrm {CW}$-complex, Trans. Amer. Math. Soc. 90 (1959), 272–280. MR 100267, DOI 10.1090/S0002-9947-1959-0100267-4
Rolf Schön, Fibrations over a CWh-base, Proc. Amer. Math. Soc. 62 (1976), no. 1, 165–166 (1977). MR 431163, DOI 10.1090/S0002-9939-1977-0431163-7
James Stasheff, A classification theorem for fibre spaces, Topology 2 (1963), 239–246. MR 154286, DOI 10.1016/0040-9383(63)90006-5
Dennis Sullivan, Genetics of homotopy theory and the Adams conjecture, Ann. of Math. (2) 100 (1974), 1–79. MR 442930, DOI 10.2307/1970841